Method of manufacturing an elongated composite diffraction grating

ABSTRACT

An economical method of manufacturing an elongated composite diffraction grating in mass production with the aid of a combination of a plurality of steps comprises replicating from a master diffraction grating a number of replica diffraction gratings, clamping the replica diffraction gratings in a jig with one of them being made stationary while the other is made adjustable so as to bring it into coincidence with the stationary one in direction and phase, and mechanically securing or cementing the gratings together.

United States Patent lnventor Kiyom Koshiishi No. 1758, Ala-Wade Tama-Machi, Minami-Tama-Gun, Tokyo, Japan Appl. No. 662,433 Filed Aug. 22, 1967 Patented Nov. 23, 1971 Priorities Aug. 26, 1966 Japan 41/55796;

Aug. 10, 1967, Japan, No. 42/50929 METHOD OF MANUFACTURING AN ELONGATED COMPOSITE DIFFRACTION GRATING Primary ExaminerCarl D. Quarforth Assistant Examiner-Stephen J. Lechert, Jr. Attorney- Waters, Roditi, Schwartz & Nissen ABSTRACT: An economical method of manufacturing an elongated composite diffraction grating in mass production with the aid of a combination of a plurality of steps comprises replicating from a master diffraction grating a number of replica difi'raction gratings, clamping the replica diffraction gratings in a jig with one of them being made stationary while the other is made adjustable so as to bring it into coincidence with the stationary one in direction and phase, and mechanically securing or cementing the gratings together,

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sum 2 0r 4 PATENTEUNUY 23 I971 SHEET 3 OF 4 Fig /2 A Length wise direction The invention relates to a method of manufacturing an elongated composite diffraction grating comprising at least two replica diffraction gratings.

In the manufacture of difiraction gratings a need often exists for much expense and high degree of precision. Particularly, it has heretofore been very difficult to manufacture an elongated diffraction grating adapted to be utilized for accurate measurement which makes use of a moire fringe produced when two diffraction gratings are placed one upon the other and for automatically controlling machine tools etc.

An object of the invention is to obviate the above disadvantages and provide an improved method of manufacturing a composite diffraction grating, and which is particularly adapted to be applied in mass production in a less expensive manner.

Another object of the invention is to provide a method of manufacturing an elongated diffraction grating adapted to be utilized for accurate measurement which makes use of a moire fringe and for automatically controlling machine tools etc.

A feature of the invention is the provision of such an improved method of manufacturing an elongated composite diffraction grating which comprises in combination replicating from a master diffraction grating a number of replica diffraction gratings, clamping these replica diffraction gratings side by side in a spaced relation in a jig and making one of the gratings stationary while the other is adjustable so as to bring the other grating into coincidence with the stationary grating in direction and phase, and mechanically securing or cementing these replica gratings together to form an elongated composite diffraction grating.

Other objects, features and advantages of the invention will become apparent of a consideration from the following description considered in conjunction with the accompanying drawing, wherein:

FIG. 1 is a perspective view showing a master diffraction grating to be used in the method according to the invention;

FIG. 2a is a diagrammatic plan view of a substrate of a replica diffraction grating and FIG. 2b is its longitudinal section;

FIG. 3a is a diagrammatic plan view of a modified form of the substrate of the replica diffraction grating and FIG. 3b is its longitudinal section;

FIG. 4 is a diagrammatic illustration of a step of the method according to the invention;

FIG. 5 is a longitudinal section showing a replica diffraction grating obtained by the step of the method according to the invention as illustrated in FIG. 4;

FIG. 6 is a longitudinal section showing a modified form of the replica diffraction grating shown in FIG. 5;

FIG. 7 is a diagrammatic illustration of another step of the method according to the invention;

FIG. 8 shows a moire fringe produced at the junction of two laminated gratings in enlarged scale;

FIG. 9 illustrates the phases of light ray diffracted by two gratings;

FIG. 10 shows a composite diffraction grating obtained by the method according to the invention with the joint being shown in section;

FIG. 11 shows a modified composite diffraction grating obtained by the method according to the invention with the joint being shown in section;

FIG. 12 is a longitudinal section of an elongated composite diffraction grating obtained by the method according to the invention;

FIG. 13 shows a diffraction grating whose gratings are inclined by an angle from the vertical;

FIG. 14 is a diagrammatic illustration of a method of testing the accuracy at the junction of a composite diffraction grating with the aid ofa moire fringe;

FIGS. 15 and 16 show moire fringes produced at the junction in different states;

FIG. 17 is a curve illustrating a buildup pitch error in a conventional composite diffraction grating;

FIGS. l8, l9 and 20 illustrate a method of manufacturing a composite diffraction grating having substantially no built-up pitch error according to the invention; and

FIG. 21 shows a curve illustrating a builbup pitch error of a composite diffraction grating obtained by the method illustrated in FIGS. 18, 19 and 20.

Referring to FIG. I, 1 designates a grating surface of a diffraction grating formed on its substrate 2 and having a length L In the method according to the invention, use is made of such diffraction grating 1, 2 as a master from which a number of replica diffraction gratings are replicated. To this end substrates 3 and 4 shown in FIGS. 2 and 3 are used as substrates for supporting replica diffraction grating surfaces to be formed thereon. The length L of these substrates 3 and 4 is made shorter than the length L of the grating surface I so as to form the replica grating surface throughout the surface of the substrates 3 and 4. The substrates 3 and 4 are subjected to machining so as to make the substrate 3 rectangular and the substrate 4 a parallelogram in longitudinal section and make the angle between the side and end edges of each of those surfaces of the substrates 3 and 4 on which the replica is to be formed right angles.

The invention makes use of an inverted L-shaped jig 5 having two vertical surfaces 5' and 5" at different levels as shown in FIG. 4. Then, the substrate 2 of the master diffraction grating is put on a horizontal base plate 6 on which the jig 5 is mounted with the two surfaces 5 and 5 thereof being directed vertically. The end surface of the substrate 2 abuts against the lower surface 5" of the jig 5. Subsequently, synthetic resin 7 is flowed over the master grating surface 1 and on the synthetic resin is placed the substrate 3 shown in FIG. 2 with its end surface being abutted against the upper surface 5 of the jig 5, thereby forming a resin replica grating 8 shown in FIG. 5. Then, the substrate 3 with its resin replica grating 8 is separated from the master grating surface I after the resin has been hardened.

The jig 5 shown in FIG. 4 is capable of obtaining a number of replica gratings whose gratings are inclined in the same direction as those of the master grating 1. Thus, the gratings of the replica diffraction grating are inclined by the same angle from the end surface of its substrate. FIG. 6 shows a replica grating 9 formed on the parallelogram-shaped substrate 4 shown in FIG. 3.

The thus obtained replica diffraction grating 3, 8 shown in FIG. 5 is clamped in a channel-shaped jig 10 through a razor blade 11 by means of a screw 12 in a manner such that one of the end and side surfaces of the replica grating 3, 8 abuts against the inner end and side surfaces of the jig 10. Then, another replica diffraction grating 3', 8' is adjustably clamped in the jig 10 by means of a pivot 13 projected from the inner surface of the jig 10, two screws 14 and 15 abutting against those parts of one side surface of the substrate 3 which are located across the pivot 13 and a micrometer 16 abutting against one end surface of another grating 3, 8' through a razor blade 17, the another end surface of the grating 3, 8 being spaced a short distance from the opposite end surface of the grating 3, 8 to form a gap g. 18 designates a place for holding the micrometer 16. Subsequently, another diffraction grating 19 having a pitch which is the same as the pitches of the replica diffraction gratings 8, 8' is placed on the latter across the gap g to form a moire fringe.

In general, when two diffraction gratings each having a pitch w are placed one upon the other with the grating of one of these two gratings being inclined by a minute angle 6 from the grating of the other diffraction grating, there is produced a moire fringe having a pitch W which is represented by the following formula If the gratings 8 and 8 are not parallel each other, the pitch W of the moire fringe produced from the diffraction gratings 19 and 8 becomes different from the pitch W of the moire produced from the diffraction gratings 19 and 8'. In the method according'to the invention the screws 14 and 15 are accurately adjusted so as to bring the pitch W of the moire fringe produced from the diffraction gratings l9 and 8' into coincidence with the pitch w of the moire fringe produced from the diffraction gratings l9 and 8 thus making the gratings of both gratings of diffraction gratings 8 and 8 parallel to each other.

The invention is capable of manufacturing a replica diffraction grating having gratings inclined by the same angle from the end surface of its substrate so that the above-mentioned difference of the pitches of the moire fringes becomes rather small. Thus it is simple to make the gratings 8 and 8 parallel to each other by adjusting the screws 14 and 15.

But, even when the gratings 8 and 8' are parallel to the moire fringes W, W are displaced at the junction g of the gratings 8 and 8 as shown in FIG. 8 if the gap g is not equal to mw, i.e.,g:='mw(where m is a positive integer and w designates a pitch of a diffraction grating), that is, if the grating 8 is not in phase with the grating 8' at the junction g.

In general, it has been theoretically proved that in the case of observing the moire fringe, the phase of light rays penetrating through two spaced diffraction gratings 8, 8' is dependent upon a relative phase of the gratings 8, 8', that is, the gap g and upon the difference between the thickness of the gratings 8, l9 and the thickness of the gratings 8', 19.

Further, it has been theoretically proved that if two diffraction gratings 20 and 21 arearranged one above the other so that zero order and first order of light rays only are intensely diffracted as shown in FIG. 9 and that the moire fringe produced thereon is observed in a direction in which the total order number is the first order, the phases of the diffracted light rays (0, +1) and (+1, are not influenced by the difference between the thicknesses of the gratings 20 and 21 when the light rays of the zero order and the first order diffracted at the diffraction grating 21 impinge upon the diffraction grating 20 such that a mutual relation between the angle made between the incident light rays and the vertical on the diffraction grating and the angle ,8 made between the diffracted light rays and the vertical satisfy the condition that ,B,= B2- Since it is difficult in practice to make the thickness of the two diffraction gratings 8 and 8 exactly equal, in accordance with the invention the moire fringe is observed in such a direction that the phase of the light ray is not influenced by the difference in the thicknesses of the gratings of the two laminated diffraction gratings, while the micrometer is accurately adjusted so as to make the gap g equal to mw, i.e., g=mw.

As explained hereinbefore the adjustments of the screws 14 and 15 so as to make the pitches of the moire fringes equal, and of the micrometer 16 so as to eliminate the displacement between these moire fringes ensure parallel direction of the gratings 8 and 8 shown in FIG. 7 and further provide the important advantage that the gap g is made equal to mw, i.e. g=mw.

In accordance with the invention, the thus adjusted gratings 8 and 8' are mechanically secured together or cemented together with the aid of the synthetic resin to form a composite diffraction grating.

An elongated diffraction grating having any desired length can be obtained by securing further replica diffraction gratings one by one in a similar manner to the diffraction gratings 8 and 8 secured or cemented together as above explained.

The smaller the gap 3 the better the composite diffraction grating obtained. But in practice there is an allowable smallest limit for the gap g. If light rays impinge upon a composite diffraction grating 22 which is rectangular in section as shown in FIG. 10 with the incident rays being inclined by an angle 7 from the line normal to the grating 22, g at the gap 23 becomes g which is represented by g"=g-cos'y (3) From formulas (2) and (3) gg' '=I' sin-y This formula shows that the use of the composite diffraction grating 24 shown in FIG. 11 ensures reduction of the influence of the gap upon the moire fringe to the extent shown by the above formula, thereby facilitating means of photoelectrically counting the amount of displacement of the moire fringe.

Another feature of the invention lies in that the composite diffraction grating obtained by the step explained with reference to FIG. 7 is used as a master, and a replica composite diffraction grating is formed on such master. The thus replicated composite diffraction grating is shown in FIG. 12 in which 26 designates gratings and 27 shows a substrate common to a number of gratings 26.

As above mentioned, the invention provides an economical way of manufacturing an elongated composite diffraction grating in mass production with the aid of a combination of a plurality of steps without incurring great expense and without using a specially designed ruling machine, and can be applied conveniently to the accurate measurement which makes use of the moire fringe and to automatic control of machine tools etc.

A further feature of the invention is that use is made of a zero-biassed diffraction grating, that is a diffraction grating whose gratings are all parallel with the line vertical to the side surface of the substrate, thus eliminating built-up pitch error to be explained hereinafter.

In general, a diffraction grating adapted for use in measuring instruments which make use of the moire fringe must be accurate not only in its relative pitch, but also in its absolute pitch value. The gratings 1 of such diffraction grating, therefore, are inclined by a small angle 4, from a line 28 vertical to the side surface of the substrate 2 for the purpose of adjusting the absolute pitch value as shown in FIG. 13. If the pitch vertical to the grating l is designated by w a desired grating constant w is given by the following formula In general, when two diffraction gratings each having a pitch constant w are placed one upon the other with the grating of one of these two gratings being inclined by a minute angle 0 from the grating of the other diffraction grating, there is a moire fringe having a pitch W which is represented by the following formula Now, two diffraction gratings 29 and 30 each having a pitch constant w are arranged side by side with a gap g being formed therebetween and another diffraction grating 31 having also a pitch constant w is placed across the gap 3 to form a moire fringe as shown in FIG. 14. The invention makes it possible to adjust the grating 30 with respect to the grating 29 and in the manner as explained with reference to FIG. 7, with the result that the gap g at the junction becomes a positive integer times larger than the grating constant w and that the gratings 29 and 30 become parallel to each other. Thus, the displacement of the moire fringe at the junction g is eliminated and the pitches of the moire fringe become equal. In practice, however, the detectable displacement of the moire fringe is W/ even when a magnifying optical lens system is used,

If it is assumed that the pitches W, Wof the moire fringe are equal to each other and that the phases at the junction are displaced W/ 10 as shown in FIG. 15, the error of the grating constant of the composite diffraction grating as a whole is only one tenth of the grating constant, which is practically negligible.

However, even if the moire fringe at the junction is in phase, the difference in the pitches of the moire fringe caused by the fact that the gratings are not in parallel, will cause the built-up pitch error of the composite diffraction grating as a whole become large so that such built-up pitch error can not be disregarded.

Now, it is considered that one of the moire pitches overlaps the other moire pitch by W/ ID as shown in FIG. 16. Assuming one of the pitch constants at both sides of the junction g as a center to be w and the other pitch constant to be w( 1+e), the pitches of the moire fringe W and W are represented by the following formulas From the above formula (4) As can be seen from the above formula 8), if the biasing angle becomes large, Ag also becomes large thus making the gratings at both sides of the junction not parallel. At the same time if use is made of a general diffraction grating having a biased angle g to manufacture a composite diffraction grating, the composite diffraction grating is much influenced by Aw. A typical built-up pitch error produced in the above mentioned composite diffraction grating is shown in FIG. 17.

In order to eliminate such built-up pitch error, the invention makes use of a number of replica diffraction gratings 32, 33 each having no biassed gratings 32 and manufactured, for example, by the step explained with reference to FIG. 4. Then, a composite diffraction grating 32, 33, 32', 33, with zero biassed gratings are replicated onto a substrate 34 as shown in FIG. 19. The composite replica diffraction grating thus manufactured has the advantages that even if the pitches at both sides of the junction g is different by W/ 10, for example, each, other A5 is smaller than that of the composite diffraction grating consisting of the biassed gratings as can be seen from the formula (8 and that Aw is less influenced since tang, is zero or substantially zero. Thus, the composite diffraction grating 35, 36 manufactured by using the above mentioned zero biassed gratings and shown in FIG. 20 has substantially no built-up pitch error as shown in FIG. 21. The method according to the invention renders it possible to manufacture a composite diffraction grating having an improved grating accuracy contrary to the conventional method of manufacturing a composite diffraction grating consisting of biassed gratings.

It will be appreciated that the invention is not restricted to the embodiments described and that many variations are possible to a person skilled in the art without departing from the scope of the invention.

What I claim is:

1. A method of manufacturing a composite diffraction grating comprising the steps of arranging a plurality of gratings replicated from a common master grating in edge to edge relation beside one another, superposing a further grating on the plurality of first gratings to produce moire fringes with the replicas, adjusting the relative position of the replicas until the moire fringes indicate that the grating lines of the replicas are parallel and in phase, and bonding the replicas in this relative position.

2. A method as claimed in claim 1 wherein each replica grating has a substrate which is shorter in length than the length of the master grating.

3. A method as claimed in claim 1 wherein each replica grating is formed with a substrate having a grating face which is rectangular.

4. Method as claimed in claim 1 wherein each replica grating is formed with a substrate longitudinal cross section of parallelogram form.

5. A method as claimed in claim 1 wherein each replica grating is formed with a substrate having a longitudinal cross section of rectangular form.

6. A method as claimed in claim 1 wherein each replica grating is formed with grating lines extending across it from side to side and two such replica gratings are clamped in a jig edge to edge in spaced relation, one of the replica gratings being clamped stationary while the other is adjustably clamped, the relative position of the gratings then being adjusted and the gratings are bonded by being cemented together.

7. A method as claimed in claim 1 wherein the common master grating is itself a composite diffraction grating prepared from a plurality of replica gratings replicated from a common master grating.

8. A method as claimed in claim 1 wherein said replica gratings are produced from the master grating by casting a resin on the master grating, securing a substrate to the thus cast resin and removing the substrate and cast resin from the master grating after hardening of the resin. 

2. A method as claimed in claim 1 wherein each replica grating has a substrate which is shorter in length than the length of the master grating.
 3. A method as claimed in claim 1 wherein each replica grating is formed with a substrate having a grating face which is rectangular.
 4. Method as claimed in claim 1 wherein each replica grating is formed with a substrate longitudinal cross section of parallelogram form.
 5. A method as claimed in claim 1 wherein each replica grating is formed with a substrate having a longitudinal cross section of rectangular form.
 6. A method as claimed in claim 1 wherein each replica grating is formed with grating lines extending across it from side to side and two such replica gratings are clamped in a jig edge to edge in spaced relation, one of the replica gratings being clamped stationary while the other is adjustably clamped, the relative position of the gratings then being adjusted and the gratings are bonded by being cemented together.
 7. A method as claimed in claim 1 wherein the common master grating is itself a composite diffraction grating prepared from a plurality of replica gratings replicated from a common master grating.
 8. A method as claimed in claim 1 wherein said replica gratings are produced from the master grating by casting a resin on the master grating, securing a substrate to the thus cast resin and removing the substrate and cast resin from the master grating after hardening of the resin. 